Magnetic nulls in interacting dipolar fields

The prominence of nulls in reconnection theory is due to the expected singular current density and the indeterminacy of field-lines at a magnetic null. Electron inertia changes the implications of both features. Magnetic field lines are distinguishable only when their distance of closest approach exceeds a distance ${\mathrm{\Delta }}_d$. Electron inertia ensures $\Delta_d\gtrsim c/\omega_{pe}$\mathrm{.}Thelinesthatliewithinamagneticfluxtubeofradius$\Delta_d$attheplacewherethefieldstrength$B$ is strongest are fundamentally indistinguishable. If the tube, somewhere along its length, encloses a point where $B=0$,vanishes, then distinguishable lines come no closer to the null than $\approx (a^{2}c\mathrm{/}{\omega }_{pe}{)}^{1\mathrm{/}3}$, where $a$ is a characteristic spatial scale of the magnetic field. The behavior of the magnetic field lines in the presence of nulls is studied for a dipole embedded in a spatially constant magnetic field. In addition to the implications of distinguishability, a constraint on the current density at a null is obtained, and the time required for thin current sheets to arise is derived.